With development of portable electronic device, battery charging system is widely used in application of portable electronic device. FIG. 1 shows a conventional battery charging system 100 employing step-down converter topology. Battery charging system 100 comprises a plurality of control loops, and each control loop comprises an error amplifier and a compensation network. Take a battery voltage control loop as an example, during each switching period, a RS flip-flop FF0 is set by a clock signal CLK to turn ON a high-side switch PM1 and turn OFF a low-side switch PM2 by a switching control signal PWM. A current following through high-side switch PM1 and an inductor L1 charges an output capacitor Cout. A battery voltage Vout increases and a feedback signal Vx1 representing battery voltage Vout increases accordingly. An error amplifier A receives feedback signal Vx1 and a battery voltage reference signal REF1, and provides an error amplifier signal Vcom1. When error amplifier signal Vcom1 decreases less than a peak signal PK, a comparison circuit CP is configured to provide a signal to reset RS flip-flop FF0, and switching control signal PWM is configured to turn OFF high-side switch PM1 and turn ON low-side switch PM2. Output capacitor Cout is configured to power a load RL and battery voltage Vout decreases. When clock signal CLK set RS flip-flop FF0 again, a new switching period starts.
As shown in FIG. 1, each control loop needs at least one error amplifier, and each error amplifier needs different compensation network for loop stability, as a result, battery charging system 100 becomes complicated, and has poor transplantation for different power stages. Besides, transition between each loop is hard to design per error amplifier signals Vcom1˜Vcomn may be very closed to each other.